Four times the cube of a number is less than the difference between forty and the number. Select the inequality that represents
2 answers:
<u>Answer:</u>
<u>Explanation:</u>
let the number be x, now we are given that four times the cube of a number which means four multiplied by the cube of number
i.e 4 multiplied by is less than the difference of 40 and the number x i.e 40 - x
x is for sure less than 40 as is less than the difference between 40 and x so if we write x - 40 then we will obtain negative value which will be greater than
.
So, the inequality obtained can be written as
You might be interested in
Answer:
a) Figure attached
b) For this case we just need to see what is the value of the function when x tnd to infinity. As we can see in our original function if x goes to infinity out function tend to 1000 and thats our limiting size.
c)
And if we find the derivate when t=1 we got this:
And if we replace t=10 we got:
d)
And then:
Step-by-step explanation:
Assuming this complete problem: "A lake is stocked with 500 fish, and the population increases according to the logistic curve p(t) = 10000 / 1 + 19e^-t/5 where t is measured in months. (a) Use a graphing utility to graph the function. (b) What is the limiting size of the fish population? (c) At what rates is the fish population changing at the end of 1 month and at the end of 10 months? (d) After how many months is the population increasing most rapidly?"
Solution to the problem
We have the following function
(a) Use a graphing utility to graph the function.
If we use desmos we got the figure attached.
(b) What is the limiting size of the fish population?
For this case we just need to see what is the value of the function when x tnd to infinity. As we can see in our original function if x goes to infinity out function tend to 1000 and thats our limiting size.
(c) At what rates is the fish population changing at the end of 1 month and at the end of 10 months?
For this case we need to calculate the derivate of the function. And we need to use the derivate of a quotient and we got this:
And if we simplify we got this:
And if we simplify we got:
And if we find the derivate when t=1 we got this:
And if we replace t=10 we got:
(d) After how many months is the population increasing most rapidly?
For this case we need to find the second derivate, set equal to 0 and then solve for t. The second derivate is given by:
And if we set equal to 0 we got:
And then:
